一种构造三水平因子超饱和设计的准则和算法

在工业统计试验和其他科学试验中,常遇到因子个数多而所允许的试验次数少的情况,这时要用到超饱和设计,以前的文章仅研究了二水平因子的超饱和设计,本文对于三水平因子的超饱和设计提出了一种基于典则相关意义下的优良性准则和构造算法,并给出了试验次数为９和１８可分别安排到２６和３０个因子的三水平超饱和设计表。     

混水平均匀设计的构造

我们用离散偏差来度量部分因子设计的均匀性,本文的目的在于寻找一些构造混水平均匀设计的方法,这些方法比文献中已有的方法更简单且计算成本更低.我们得到了离散偏差的一个下界,如果一个U 型设计的离散偏差值达到这个下界,那么该设计是—个均匀设计.我们建立了均匀设计与组合设计理论中一致可分解设计之间的联系.通过一致可分解设计,我们提出了一些构造均匀设计的新方法,同时也给出了许多均匀设计存在的无穷类.     

几个对参数设计有用的正交表

本文给出对参数设计有用的几个正交表Ｌ′１６（２１２），Ｌ′１６（２１４），Ｌ３６（２１１×３１２），Ｌ１０８（３４９），Ｌ１０８（２３×３４９），Ｌ１０８（２１１×３４８）和Ｌ１０８（２３５×３３６）这些正交表不包含交互作用列，适合于参数设计使用。本文还将证明Ｌ４５（３２２）和Ｌ６３（３３１）的不可能性。     

CONSTRUCTION OF OPTIMAL BLOCKING SCHEMES FOR ROBUST PARAMETER DESIGNS

Robust parameter design (RPD) is an important issue in experimental designs. If all experimental runs cannot be performed under homogeneous conditions, blocking the units is effective. In this paper, w...     

APPLICATION OF MINIMUM PROJECTION UNIFORMITY CRITERION IN COMPLEMENTARY DESIGNS

In this article, we consider the characterization problem in design theory. The objective is to characterize minimum projection uniformity for two-level designs in terms of their complementary designs. Here, the complementary design means a design in which all the Hamming distances of any two runs are the same, which generalizes the concept of a pair of complementary designs in the literature. Based on relationships of the uniformity pattern between a pair of complementary designs, we propose a minimum projection uniformity （MPU） rule to assess and compare two-level factorials.     

A CASE STUDY IN THE APPLICATION OF SUPERSATURATED DESIGNS TO COMPUTER EXPERIMENTS

Supersaturated design is essentially a fractional factorial design in which the number of potential effects is greater than the number of runs. In this article, the supersaturated design is applied to a computer experiment through an example of steady current circuit model problem. A uniform mixed-level supersaturated design and the centered quadratic regression model are used. This example shows that supersaturated design and quadratic regression modeling method are very effective for screening effects and building the predictor. They are not only useful in computer experiments but also in industrial and other scientific experiments.     

完全组内平衡区组设计的性质及应用

本文研究了完全组内平衡性的相关哲学概念和数学性质.利用多边矩阵理论,证明了完全组内平衡区组设计的数学判定条件,给出了计算机验证完全组内平衡性的方法,推广了正交表的平衡性质.     

EMBEDDINGS OF SIMPLE TWO-FOLD BALANCED INCOMPLETE BLOCK DESIGNS WITH BLOCK SIZE FOUR

The necessary and sufficient conditions for the existence of simple incomplete block design (v, w; 4,2)-IPBDs are determined. As a consequence, the necessary and sufficient conditions for the embeddings of simple two-fold balanced incomplete block designs with block size 4 are also determined.     

CONSENSUS FORMATION OF TWO-LEVEL OPINION DYNAMICS

Opinion dynamics have received significant attention in recent years. This paper proposes a bounded confidence opinion model for a group of agents with two different confidence levels. Each agent in the population is endowed with a confidence interval around her opinion with radius αd or(1- α)d, where α∈(0, 1/2] represents the differentiation of confidence levels. We analytically derived the critical confidence bound dc = 1/(4α) for the two-level opinion dynamics on Z. A single opinion cluster is formed with probability 1 above this critical value regardless of the ratio p of agents with high/low confidence. Extensive numerical simulations are performed to illustrate our theoretical results. Noticed is a clear impact of p on the collective behavior: more agents with high confidence lead to harder agreement. It is also experimentally revealed that the sharpness of the threshold dc increases with α but does not depend on p.     

COMPUTATION OF THE E(s2) VALUES OF SOME E(s2) OPTIMAL SUPERSATURATED DESIGNS

1 IntroductionAn rerun design for m two-level faCtors is saturated if n = m 1. Such designs haveminimum number of runs for estimating all the main effects when the interactions are negligible,and are useful for screening experiments in the initial stage of an investigation where the primarygoal is to identify the few active faCtors from a large number of potential faCtors. And whelln < in 1, such designs are called supersaturated designs, which provide more flexibility andcost saving. No…     

Symmetric ‐Designs and ‐Difference Sets

In this paper, we introduce a method to construct ‐designs, which are also known as partial geometric designs, by using subsets of certain finite groups. We introduce the concept of ‐difference sets and investigate the existence and nonexistence of these structures. We also provide some nonexistence results on ‐designs based on the fact that ‐designs yield directed strongly regular graphs.     

BOUND ON THE MAXIMUM NUMBER OF CLEAR TWO-FACTOR INTERACTIONS FOR 2n-(n-k) DESIGNS

Clear effects criterion is an important criterion for selecting fractional factorial designs [1]. Tang et al. [2] derived upper and lower bounds on the maximum number of clear two-factor interactions (2fi's) in 2n-(n-k) designs of resolution Ⅲ and Ⅳ by constructing 2n-(n-k) designs. But the method in [2] does not perform well sometimes when the resolution is III. This article modifies the construction method for 2n-(n-k) designs of resolution Ⅲ in [2]. The modified method is a great improvement on that used in [2].     

CONSTRUCTING UNIFORM DESIGNS WITH TWO- OR THREE-LEVEL

When the number of runs is large, to search for uniform designs in the sense of low-discrepancy is an NP hard problem. The number of runs of most of the available uniform designs is small (≤50). In this article, the authors employ a kind of the so-called Hamming distance method to construct uniform designs with two- or three-level such that some resulting uniform designs have a large number of runs. Several infinite classes for the existence of uniform designs with the same Hamming distances between any distinct rows are also obtained simultaneously. Two measures of uniformity, the centered L2-discrepancy (CD, for short) and wrap-around L2-discrepancy (WD, for short), are employed.     

Paley type partial difference sets in abelian groups

Partial difference sets with parameters $\left(v,k,\lambda ,\mu \right)=\left(v,\left(v?1\right)/2,\left(v?5\right)/4,\left(v?1\right)/4\right)$ are called Paley type partial difference sets. In this note, we prove that if there exists a Paley type partial difference set in an abelian group of order v, where v is not a prime power, then $v=n^4$ or $9n^4$, $n>1$ an odd integer. In 2010, Polhill constructed Paley type partial difference sets in abelian groups with those orders. Thus, combining with the constructions of Polhill and the classical Paley construction using nonzero squares of a finite field, we completely answer the following question: “For which odd positive integers $v>1$, can we find a Paley type partial difference set in an abelian group of order $v$?”     

无重复因析试验中散度效应的ML估计

在无重复因析试验中,若因子A,B的散度效应显著,则不论其交互效应AB的散度效应是否显著,其散度效应的现有估计常常是有偏的,从而导致其被错误地识别为显著效应.提出了散度效应的一种新的估计方法(称为ML估计),并给出了ML估计的方差的精确表达形式,证明了在一类模型中,交互效应AB的散度效应的ML估计是无偏的.最后,将ML估计与现有的常用估计进行了比较.     

CONSTRUCTION OF GEOMETRIC PARTIAL DIFFERENTIAL EQUATIONS FOR LEVEL SETS

Geometric partial differential equations of level-set form are usually constructed by a variational method using either Dirac delta function or co-area formula in the energy functional to be minimized. However, the equations derived by these two approaches are not consistent. In this paper, we present a third approach for constructing the level-set form equations. By representing various differential geometry quantities and differential geometry operators in terms of the implicit surface, we are able to reformulate three classes of parametric geometric partial differential equations （second-order, fourth-order and sixth- order） into the level-set forms. The reformulation of the equations is generic and simple, and the resulting equations are consistent with their parametric form counterparts. We further prove that the equations derived using co-area formula are also consistent with the parametric forms. However, these equations are of much complicated forms than these given by the equations we derived.     

THE STRUCTURE AND APPROXIMATION OF A.S. SELF-SIMILAR SET

The structure of any a.s. self-similar set K(w) generated by a class of random elements {gn,wσ} taking values in the space of contractive operators is given and the approximation of K(w) by the fixed points {Pn,wσ} of {gn,ow} is obtained. It is useful to generate the fractal in computer.     

用罚函数求解二层凸规划的方法

用罚函数法将二层凸规划化为约束区域为凸集的凹规划,然后用渐进外逼算法求其全局最优解。     

复因子析因试验在半成品竹笋脱硫中的应用

通过半成品竹笋在２个不同漂洗（Ｂ因子，水平数ｍ为２）时间后，利用４个不同浓度（Ａ因子，水平数ｋ为４）的柠檬酸溶液热烫２０ｍｉｎ，再进行３个不同时间的漂洗（Ｃ因子，水平数Ｑ为３）的脱硫试验，介绍４×２×３析因试验设计与统计分析方法。     

一类齐次Moran集维数的不连续性

丰德军等人在他们的相关的论文中介绍了齐次均匀康托集和偏齐次均匀康托集,在本文中我们构造介于两者之间的一类齐次Moran集,给出其豪斯多夫维数的精确计算公式,并讨论维数关于参数的不连续性.